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variations if the base site is located in the normal magnetic field (in a horizontally
homogeneous zone). Otherwise the effect of inhomogeneities situated at the base
site will be transferred to the entire survey area and superimposed on the effects of
inhomogeneities situated at the observation sites.
Let the base site be located in the horizontally homogeneous zone. Assume that
the area under investigation contains a two-dimensional structure and the
x
−
axis
runs along the strike of this structure. Then
M
10
0
0
[
M
]
=
=
,
(4
.
47)
M
⊥
M
⊥
0
where
M
=
/
=
1 and
M
⊥
=
/
H
x
(
r
)
H
x
(
r
B
)
H
y
(
r
)
H
y
(
r
B
). Here the necessary
conditions for the two-dimensionality are observed:
=
M
xy
−
M
yx
S
w
=
.
ske
0
(4
48)
M
xx
+
M
yy
and
Im (
M
xy
M
yx
)
M
yy
+
M
xx
B
M
xx
+
M
yy
ske
w
=
=
0
,
(4
.
49)
B
are magnetic asymmetry parameters (analogs of the Swift
and Bahr parameters) and bars denote the complex conjugation.
If the base site is located in a quasi-homogeneous layered zone and conditions
ske
S
where
ske
w
and
ske
w
S
B
0 are fulfilled at some observation sites, one can suppose
that the medium under investigation is two-dimensional (quasi-two-dimensional)
and determine its principal (longitudinal and transverse) directions from the equa-
tion
w
≈
0 and
ske
w
≈
M
xy
+
M
yx
tan 2
=
Re
M
xx
.
(4
.
50)
M
yy
−
This is the simplest solution of the eigenstate problem. Its accuracy can be easily
estimated comparing the longitudinal and transverse directions obtained at different
sites.
Generally the eigenstate problem for the horizontal magnetic tensor [
M
] can be
solved by one of the methods considered in Chap. 2.
Let us adopt the Swift-Eggers method. We will look for the collinear magnetic
eigenfields
H
τ
m
(
r
) and
H
τ
m
(
r
B
),
m
=
1
,
2:
=
m
H
τ
m
(
r
B
)
,
=
,
,
.
H
τ
m
(
r
)
m
1
2
(4
51)
